Abstracts
Ivan Booth, Memorial University
Lessons from distorted black holes
This talk will review some of my work with distorted black hole spacetimes
and consider the implications for the mathematical and physical characterization
of black holes, the range of possible horizon geometries and black hole
mechanics. The distorted spacetimes are drawn from the Weyl and Ernst families
of exact solutions and include Schwarzschild, Reissner-Nordström, and
Kerr-Newman black holes distorted by gravitational and electromagnetic fields.
While the boundaries of these black holes continue to obey the theorems
constraining extremal and near-extremal horizons, they need be neither event
horizons nor marginally trapped surfaces and may be highly distorted compared
to the asymptotically flat seed solutions from which they are generated.
Some physical quantities (horizon area, charge and angular momentum) remain
well-defined however others (mass, surface gravity, Coulomb potential and
angular velocity) do not. I will examine the implications for black hole
mechanics.
Robert Brandenberger, McGill University
Towards an Effective Energy Momentum Tensor for Black Hole Evaporation
In an accelerating cosmological space-time the growth of fluctuations
on super-Hubble scales drains energy for the cosmological background and
acts to neutralize the agent which is providing the accelerated expansion.
I will discuss the effective energy-momentum tensor for cosmological perturbations
which can be used to study this back-reaction effect. I will then suggest
that a similar formalism can be used to study black hole evaporation. There
will also be a short "teaser" related to the mystery of the origin
of super-massive high redshift black holes.
Ramin Daghigh, Metropolitan State University
High Overtone Quasinormal Modes of Analog Black Holes and the Small Scale
Structure of the Background Fluid
The goal of this work is to build a foundation for, and explore
the possibility of, using high overtone quasinormal modes of analog black
holes to probe the small scale (microscopic) structure of a background fluid
in which an analog black hole is formed. This may provide a tool to study
the small scale structure of some interesting quantum systems such as Bose-Einstein
condensates.
Grigorios Fournodavlos, University of Toronto
Partial stability of a (real) Schwarzschild singularity
We will discuss how one can produce non-spherically symmetric Einstein
vacuum spacetimes containing a singularity of Schwarzschild type by realizing
a backward construction plan.
Valeri Frolov, University of Alberta
Point charge near a black hole: Bi-conformal symmetry and bi-conformal
anomaly
We study a field of a point charge at rest near a higher dimensional static
black hole. It is shown that the field equations possess, so called, biconformal
symmetry. This symmetry allows one to relate this problem to a similar problem
in the Bertotti-Robertson metric, which has enhanced symmetry. Using this
approach we obtained a useful representation for a static Green function
for a point charge near higher-dimensional Tangherlini and Reissner-Norstrom
black holes. Exact expressions for scalar massless and electric fields of
point charges in the spacetime of static 5 dimensional black holes are obtained.
We also discuss applications of the obtained results to the problem of self-energy
and self-force, bi-conformal anomalies, and fields and self-force of charges
in the homogeneous gravitational field.
Daniel Green, University of Toronto
The Present and Future of Cosmology
The past decade has seen incredible progress in observational cosmology.
Primarily from the cosmic microwave background, we have measured our many
properties of our cosmic history with a sub-percent level precision. I will
review our current understanding of the universe that has been provided
by these observations and discuss the future directions of the field over
the next decade.
Stephen Green, Perimeter Institute for Theoretical
Physics
Quasi-periodic solutions and AdS (in)stability
We consider the dynamics of a spherically symmetric massless scalar field
coupled to general relativity in anti–de Sitter spacetime in the small-amplitude
limit. We first develop the "two time framework" (TTF) approximation
to study the leading self-gravitating effects of the scalar field. This
framework allows us to rapidly obtain approximate solutions to the Einstein-scalar
system. Within TTF, we also uncover the presence of 3 conserved quantities:
the energy E, the particle number N, and the Hamiltonian H. Simultaneous
conservation of E and N implies that weakly turbulent processes undergo
dual cascades (direct cascade of E and inverse cascade of N or vice versa),
and it rules out energy equipartition for generic initial data. Finally,
TTF leads us to uncover a large class of quasi-periodic solutions, and we
discuss their role as possible islands of stability.
Coauthors: Alex Buchel, Luis Lehner, Steven L. Liebling, Antoine Maillard
Gary Horowitz, University of California, Santa
Barbara
Hovering Black Holes
I describe a new class of asymptotically anti-de Sitter charged black holes
that have recently been constructed numerically. These black holes exhibit
some surprising universality properties which are not yet understood analytically.
Using the remarkable gauge/gravity duality, they have applications to localized
defects in special condensed matter systems.
Coauthors: Nabil Iqbal, Jorge Santos and Benson Way.
Uzair Hussain, Memorial University
Master equations and the boundary stress tensor for Ads4-Schwarzschild
blackholes
We revisit the problem of perturbations of Schwarzschild-AdS$_4$ black
holes by using a combination of the Martel-Poisson gauge-invariant formalism
for perturbations of Schwarzschild [gr-qc/0502028] and the Kodama-Ishibashi
formalism [hep-th/0305147]. We clarify the relationship between both formalisms
and calculate the boundary stress tensor, $T^\mu_\nu$, on a constant-\emph{r}
surface purely in terms of the even and odd master functions. Invoking the
conservation equations $\nabla_\mu T^\mu_\nu =0$ on such a constant-\emph{r}
surface we find that the wave equations for both the even and odd master
functions are equivalent to the conservation of stress energy along directions
tangent to spherical symmetry. This direct comparison of the master equations
and the conservation equations is presented explicitly for the first time.
We also calculate the renormalized stress tensor at the boundary $\frac{r}{L}
\lim_{r \rightarrow \infty} T_{\mu\nu}$ by using our expressions for the
stress tensor in terms of the master function and demonstrate the fluid/gravity
duality for large black holes. We also investigate the possibility of a
Cotton tensor/stress tensor duality, on a constant-$r$ surface, motivated
by the duality being held at $r\rightarrow\infty$ [arXiv:0809.4852v2].
Coauthors: Ivan Booth (Memorial University) Hari Kunduri (Memorial University)
Alexandru Ionescu, Princeton University
On the stability of the wave-map equation in Kerr spaces
I will discuss some recent work on the stability of the wave-map equation
in Kerr spaces with small angular momentum. This problem should be viewed
in the context of the larger stability/rigidity problem for the family
of Kerr spaces. The talk is based on joint work with Alexakis and Klainerman.
Soichiro Isoyama, University of Guelph
Hamiltonian Dynamics of Self-Forced Motion in Kerr Spacetime
Post-geodesic motion of a point particle in Kerr spacetime subjected
to the back reaction of its own perturbation field, namely self-force,
is an important subject to model an inspiral of stellar-mass compact object
into a massive black hole, with application to gravitational astronomy.
To establish an efficient scheme to compute such binary dynamics in the
extreme mass ratio limit, we develop a Hamiltonian formulation of the
self-force dynamics in Kerr spacetime by describing them as geodesic motion
in a certain locally defined effective spacetime. In this talk, focusing
on the conservative dynamics, we show that the perturbed Hamiltonian system
is effectively "integrable" for most generic stable bound orbits;
there exists the perturbed version of action variables for geodesic motion
in Kerr spacetime, which are conserved along the orbit. Based on the``integrable''
Hamiltonian, we also sketch to compute the frequency shift of the inner
most stable inclined circular orbit, which provides a potentially observable
effect of the conservative self-force effect, and present its numerical
result in the equatorial circular limit.
Coauthors: Ryuichi Fujita, Alexandre Le Tiec, Hiroyuki Nakano, Norichika
Sago and Takahiro Tanaka
David Kubiznak, Perimeter Institute for Theoretical
Physics
Ultraspinning limits and super-entropic black holes
By employing the new ultraspinning limit we construct novel classes of
black holes in four and higher dimensions with non-compact event horizons
and finite horizon area. Our ultraspinning limit can be understood as a
simple generating technique that consists of three steps: i) transforming
the known rotating AdS black hole solution to a special coordinate system
that rotates (in a given 2-plane) at infinity ii) boosting this rotation
to the speed of light iii) compactifying the corresponding azimuthal direction.
In so doing we qualitatively change the structure of the spacetime since
it is no longer possible to return to a frame that does not rotate at infinity.
The obtained black holes have non-compact horizons with topology of a sphere
with two punctures. The entropy of some of these exceeds the maximal bound
implied by the reverse isoperimetric inequality, such black holes are super-entropic.
Coauthors: Robie Hennigar, Robert B. Mann, Nathan Musoke
Hari Kunduri, Memorial University
New Black Holes in Five Dimensions
We will discuss a new asymptotically flat, supersymmetric black hole solution
to five-dimensional supergravity. This solution is regular on and outside
an event horizon of lens-space topology L(2,1) and is the first example
of an asymptotically flat black hole with lens-space topology. The geometry
is characterized by a charge, two angular momenta, and a magnetic flux though
a non-contractible disc region ending on the horizon. In addition, we will
discuss a second new family of solutions describing a spherical black hole
with a two-cycle in the exterior region. We show there are black holes in
this family with identical conserved changes to the BMPV black hole, thereby
demonstrating black hole non-uniqueness in this context.
Coauthors: James Lucietti
Philippe Landry, University of Guelph
Tidal Deformation of a Slowly Rotating Compact Body
The deformation of a compact body subject to weak, slowly varying tidal
forces is characterized by a set of dimensionless, equation-of-state-dependent
constants known as tidal Love numbers. If the body in question is non-rotating,
its gravitational response to a generic quadrupolar tidal field is encoded
in two of these constants: the gravitoelectric Love number k₂ᵉˡ
and the gravitomagnetic Love number k₂ᵐᵃᵍ.
If, however, the body is rotating – as is typically the case in astrophysical
scenarios – coupling between its angular momentum vector and the tidal
field complicates its response. The problem is tractable in the slow-rotation
limit, and four additional quantities, designated tidal-rotational Love
numbers, are required to give a complete description of the body's deformation.
These new Love numbers are shown to vanish when the body is a black hole.
Coauthors: Eric Poisson
Geoffrey Lovelace, California State University,
Fullerton
Nearly extremal apparent horizons in numerical simulations of colliding
black holes
The spin $S$ of a Kerr black hole is bounded by the surface area $A$ of
its apparent horizon: $8 \pi S \leq A$. In this talk, we will present recent
results (arXiv:1411.7297) for the extremality of apparent horizons for merging,
rapidly rotating black holes with equal masses and equal spins aligned with
the orbital angular momentum. Measuring the area and (using approximate
Killing vectors) the spin on the individual and common apparent horizons,
we find that the inequality $8 \pi S < A$ is satisfied but is very close
to equality on the common apparent horizon at the instant it first appears---even
for initial black-hole spins as large as $S/M^2=0.994$. We introduce a gauge-invariant
lower bound $e_0$ on the extremality by computing the smallest value that
Booth and Fairhurst's extremality parameter can take for any scaling of
the horizon's null normal vectors, concluding that the common horizons are
at least moderately close to extremal just after they appear. We construct
binary-black-hole initial data with marginally trapped surfaces with $8
\pi S > A$ and $e_0 > 1$, but these surfaces are always surrounded
by apparent horizons with $8 \pi S < A$ and $e_0 < 1$.
Coauthors: Mark A. Scheel, Robert Owen, Matthew Giesler, Reza Katebi, Bela
Szilagyi, Tony Chu, Nicholas Demos, Daniel A. Hemberger, Lawrence E. Kidder,
Harald P. Pfeiffer, Nousha Afshari
Jonathan Luk, University of Cambridge
The stability of the Kerr Cauchy horizon and the strong cosmic censorship
conjecture in general relativity
I will discuss recent work on the structure of black hole interiors
for dynamical vacuum spacetimes (without any symmetry) and what this means
for the question of the nature of generic singularities in general relativity
and the celebrated strong cosmic censorship of Penrose. This is joint
work with Mihalis Dafermos.
Raissa Mendes, University of Guelph
On the possibility of setting a new constraint to scalar-tensor theories
Scalar-tensor theories are a widely studied alternative to general relativity
in which gravity is endowed with an additional scalar degree of freedom.
Although severely constrained by solar system and pulsar timing experiments,
there remains a large set of scalar-tensor theories which are consistent
with all present day observations. In this poster, I discuss a recent result
[PRD 91, 064024 (2015)] on the possibility of probing a yet unconstrained
region of the parameter space of scalar-tensor theories based on the fact
that stability properties of highly compact neutron stars in these theories
may radically differ from those in general relativity.
Jonas Mureika, Loyola Marymount University
Sub-Planckian Black Holes and the Generalized Uncertainty Principle
The generalized uncertainty principle suggests there is a minimum mass
for a black hole, or alternatively a maximum particle mass ($M = M_{\rm
Pl}$). The prospect of sub-Planckian black holes ($M \ll M_{\rm Pl}$) is
explored in the context of a new self-dual, Schwarzschild-like metric that
encodes features of the GUP. It is shown that not only do sub-Planckian
black holes exist in this scenario, but that they are governed by what appears
to be an effectively (1+1)-dimensional gravitational theory. This adds support
to the notion that dimensional reduction is an expected feature of quantum
gravity.
Coauthors: Bernard Carr, Piero Nicolini
Maria Okounkova, California Institute of Technology
Numerical Tests of the Cosmic Censorship Conjecture via Event-Horizon Finding
We present the current state of our research on the possibility
of naked singularity formation in gravitational collapse, numerically testing
both the cosmic censorship conjecture and the hoop conjecture. The former
of these posits that all singularities lie behind an event horizon, while
the later conjectures that this is true if collapse occurs from an initial
configuration with all circumferences C = 4 pi M. We reconsider the classical
Shapiro & Teukolsky (1991) prolate spheroid naked singularity scenario.
Using the exponentially error-convergent Spectral Einstein Code (SpEC) we
simulate the collapse of collisionless matter and probe for apparent horizons.
We propose a new method to probe for the existence of an event horizon by
following characteristic from regions near the singularity, using methods
commonly employed in Cauchy characteristic extraction.
Coauthors: Mark Scheel, Yanbei Chen
Amanda Peet, University of Toronto
String modelling of black holes and holography
The string theory approach to quantum gravity forms the context for our
discussion of two interrelated themes: microscopic string modelling of black
holes, and AdS/CFT holography.
A 2009 result of S.Mathur showed that the black hole information paradox
cannot be resolved via semiclassical perturbation theory. Starting from
the microscopic SCFT of the prototype D1-D5-brane system in a top-down approach,
we use conformal perturbation theory to explore aspects of deforming towards
the classical black hole geometry.
Our second theme recruits a more bottom-up motivation to explore holographic
setups with increasing amounts of broken symmetry. We discuss modelling
disorder holographically for the charged case, using perturbation theory
in disorder strength to construct solutions including gravitational backreaction,
and find the conductivity.
This talk will be pitched at colloquium level and will assume no prior
knowledge of string theory.
Paolo Pani, Sapienza University of Rome
Tidal deformations of a spinning compact object
The deformability of a compact object induced by a perturbing tidal field
is encoded in the tidal Love numbers, which depend sensibly on the object's
internal structure. Tidal Love numbers are known only for static, spherically-symmetric
objects. As a first step to compute the tidal Love numbers of a spinning
compact star, here we extend powerful perturbative techniques to compute
the geometry of a tidally-distorted spinning object to second order in the
angular momentum. The spin of the object introduces couplings between electric
and magnetic deformations and new classes of induced Love numbers emerge.
For example, a spinning object immersed in a quadrupolar, electric tidal
field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole
moments to second order in the spin. The deformations are encoded in a set
of inhomogeneous differential equations which, remarkably, can be solved
analytically in vacuum. We prove that the tidal Love numbers of a Kerr black
hole are zero to second order in the spin and provide the explicit solution
for a slowly-rotating, tidally-deformed Kerr black hole.
Coauthors: Leonardo Gualtieri, Andrea Maselli, Valeria Ferrari
Adam Pound, University of Southampton
Point particle perturbations in Kerr spacetime: reconstruction, completion,
and self-force
Computing the metric perturbation produced by a point particle moving around
a Kerr black hole, and finding the back-reaction of that perturbation on
the particle's motion, is an important problem in GR, with applications
to both gravitational wave astronomy and fundamental physics. Since the
1970s, there has been a standard, efficient method of obtaining metric perturbations
in a Kerr background by reconstructing them from a Weyl curvature scalar.
However, when a point particle is introduced into this reconstruction procedure,
gauge singularities arise that extend away from the particle, significantly
complicating the definition and calculation of the gravitational self-force
(i.e., the back-reaction). Furthermore, the reconstruction procedure does
not uniquely determine the metric perturbation, instead leaving the freedom
to add "trivial" perturbations that shift the spacetime's mass
and angular momentum; because the particle's orbit divides the spacetime
into two regions, one must "complete" the reconstructed perturbation
by finding the correct mass and angular momentum perturbations to add inside
and outside the orbit. In this talk I describe recent work that establishes
the correct "completion" terms and a rigorous method of computing
the self-force (and related quantities) from the reconstructed and completed
metric.
Coauthors: Cesar Merlin Gonzalez, Leor Barack, Amos Ori, Abhay Shah, and
Maarten van de Meent
Parthapratim Pradhan, Vivekananda Satavarshiki
Mahavidyalaya
Enthalpy and Geometric Volume for Van der Waals Black Hole \
Interpreting the negative cosmological constant as a dynamical pressure
and the volume is its thermodynamically conjugate variable then the gravitational
mass could be expressed as the total gravitational enthalpy rather than
the energy. A new phenomena then emerges in the context of extended phase
space thermodynamics. We \emph{examine} here these features for recently
discovered Van der Waal black hole which is analogous to the Van der Waals
fluid. We show that the thermodynamic volume is \emph{greater} than the
naive geometric volume. We also show that the Smarr-Gibbs-Duhem relation
is \emph{satisfied} for this black hole. Furthermore, by computing the specific
heat we find the stability criterion for this black hole. It has been observed
that under certain condition the black hole displays the \emph{second order
phase transition}.
Frans Pretorius, Princeton University
Eccentric Mergers
Binary compact object mergers are among the primary gravitational wave
sources expected to be observed by the next generation of ground-based gravitational
wave detectors. Early success of this endeavour will to a large extent depend
on how well we can model these events. I will discuss a class of compact
object binaries that arise from dynamical capture in dense cluster environments.
The typical merger from this class of event will differ from a traditional
primordial binary in that the initial orbit will be highly eccentric, and
when neutron stars are involved the neutron stars could have high spin.
Even if, as expected, such events are rare, they could offer exceptional
laboratories to learn about general relativity in the dynamical strong-field
regime, and with neutron stars could host unusually bright electromagnetic
counterparts. However, to realize this potential of eccentric systems will
requiring overcoming some significant challenges in modelling them.
Volker Schlue, University of Toronto
Non-existence of time-periodic dynamics in general relativity
In general relativity, a self-gravitating system is not expected to display
time-periodic behavior due to the emission of gravitational waves. We show
that any asymptotically flat solution to the Einstein vacuum equations,
which is assumed to be time-periodic, is in fact stationary near infinity.
Thus genuinely time-periodic vacuum space-times do not exist, at least far
away from the sources. The proof applies under physically relevant smoothness
assumptions, and employs a uniqueness theorem for linear waves obtained
jointly with S. Alexakis and A. Shao.
Coauthors: Spyros Alexakis
Saul Teukolsky, Cornell University
Simulations of Black Holes and Neutron Stars
Advanced LIGO will conduct its first science run this summer.
One of the prime scientific goals is to detect waves from the coalescence
and merger of black holes and neutron stars in binary systems. Confronting
such signals with the predictions of Einstein's General Theory of Relativity
will be the first real strong-field test of the theory. I will describe
the status of numerical simulations of such systems, which have set things
up for an epic confrontation between theory and experiment. I will also
describe the limitations of current codes for computational astrophysics
and the ingredients of a next-generation code for upcoming exascale machines.
William Unruh, University of British Columbia
Partners
Black holes evaporate sending out thermal incoherent radiation which can
be detected by detectors. But those particles each have a partner, which
purifies the state. Ie, for each detected particle mode there is another
one which is maximally entangled with it. We derive this mode, show that
the relation is not linear, use it to ask about the partner of detector
excited by the vacuum, and argue that in some cases, the partner can be
a vacuum fluctuation. This may have some relation to the question of black
hole "Unitarity".
Robert Wald, University of Chicago
Dynamic and Thermodynamic Stability of Black Holes and Black Branes
I describe work with Stefan Hollands that establishes a new criterion for
the dynamical stability of black holes and black branes with respect to
axisymmetric perturbations. Our analysis is done in vacuum general relativity
without a cosmological constant in $D \geq 4$ spacetime dimensions, but
our approach is applicable to much more general situations. We show that
the positivity of the canonical energy, $\mathcal E$, on a subspace of linearized
solutions that have vanishing linearized ADM mass and angular momentum implies
mode stability. Conversely, failure of positivity of canonical energy on
this subspace implies instability in the sense that there exist perturbations
that cannot asymptotically approach a stationary perturbation. We further
show that the canonical energy is related to the second order variations
of mass, angular momentum, and horizon area by $\mathcal E = \delta^2 M
- \sum_i \Omega_i \delta^2 J_i - (\kappa/8\pi) \delta^2 A$. This establishes
that dynamic stability of a black hole is equivalent to its thermodynamic
stability (i.e., its area, $A$, being a maximum at fixed ``state parameters''
$M$, $J_i$). For a black brane, we further show that a sufficient condition
for instability is the failure of the Hessian of $A$ with respect to $M$,
$J_i$ to be negative, thus proving a conjecture of Gubser and Mitra. We
also prove that positivity of $\mathcal E$ is equivalent to the satisfaction
of a ``local Penrose inequality,'' thus showing that satisfaction of this
local Penrose inequality is necessary and sufficient for dynamical stability.
S.T. Yau, Harvard University
General Relativity and Mathematics
Exactly one century ago, Einstein wrote down his famous equation that
governs gravity and the dynamical spacetime. I will describe the mathematics
behind Einstein's work and its influence to modern development of geometry,
analysis and string theory. I will talk about our recent work on defining
quasi-local mass in general relativity, which has been developed in collaboration
with Mu-Tao Wang and Po-Ning Chen.
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