89 research outputs found
Boundary Counterterms and the Thermodynamics of 2-D Black Holes
We utilize a novel method to study the thermodynamics of two dimensional type
0A black holes with constant RR flux. Our approach is based on the
Hamilton-Jacobi method of deriving boundary counterterms. We demonstrate this
approach by recovering the standard results for a well understood example,
Witten's black hole. Between this example and the 0A black hole we find
universal expressions for the entropy and black hole mass, as well as the
infra-red divergence of the partition function. As a non-trivial check of our
results we verify the first law of thermodynamics for these systems. Our
results for the mass disagree with the predictions of a proposed matrix model
dual of the 0A black hole.Comment: 27 pages, uses utarticle.cls; corrected typos and added reference
Extremal Black Holes in Dynamical Chern-Simons Gravity
Rapidly rotating black hole solutions in theories beyond general relativity
play a key role in experimental gravity, as they allow us to compute
observables in extreme spacetimes that deviate from the predictions of general
relativity. Such solutions are often difficult to find in
beyond-general-relativity theories due to the inclusion of additional fields
that couple to the metric non-linearly and non-minimally. In this paper, we
consider rotating black hole solutions in one such theory, dynamical
Chern-Simons gravity, where the Einstein-Hilbert action is modified by the
introduction of a dynamical scalar field that couples to the metric through the
Pontryagin density. We treat dynamical Chern-Simons gravity as an effective
field theory and work in the decoupling limit, where corrections are treated as
small perturbations from general relativity. We perturb about the
maximally-rotating Kerr solution, the so-called extremal limit, and develop
mathematical insight into the analysis techniques needed to construct solutions
for generic spin. First we find closed-form, analytic expressions for the
extremal scalar field, and then determine the trace of the metric perturbation,
giving both in terms of Legendre decompositions. Retaining only the first three
and four modes in the Legendre representation of the scalar field and the
trace, respectively, suffices to ensure a fidelity of over 99% relative to full
numerical solutions. The leading-order mode in the Legendre expansion of the
trace of the metric perturbation contains a logarithmic divergence at the
extremal Kerr horizon, which is likely to be unimportant as it occurs inside
the perturbed dynamical Chern-Simons horizon. The techniques employed here
should enable the construction of analytic, closed-form expressions for the
scalar field and metric perturbations on a background with arbitrary rotation.Comment: 25+9 pages (single column), 10 figures, 1 table; matches published
versio
Black Hole Thermodynamics and Hamilton-Jacobi Counterterm
We review the construction of the universal Hamilton-Jacobi counterterm for
dilaton gravity in two dimensions, derive the corresponding result in the
Cartan formulation and elaborate further upon black hole thermodynamics and
semi-classical corrections. Applications include spherically symmetric black
holes in arbitrary dimensions with Minkowski- or AdS-asymptotics, the BTZ black
hole and black holes in two-dimensional string theory.Comment: 9 pages, proceedings contribution to QFEXT07 submitted to IJMPA, v2:
added Re
Finite Charges from the Bulk Action
Constructing charges in the covariant phase formalism often leads to formally
divergent expressions, even when the fields satisfy physically acceptable
fall-off conditions. These expressions can be rendered finite by corner
ambiguities in the definition of the presymplectic potential, which in some
cases may be motivated by arguments involving boundary Lagrangians. We show
that the necessary corner terms are already present in the variation of the
bulk action and can be extracted in a straightforward way. Once these corner
terms are included in the presymplectic potential, charges derived from an
associated codimension-2 form are automatically finite. We illustrate the
procedure with examples in two and three dimensions, working in Bondi gauge and
obtaining integrable charges. As a by-product, actions are derived for these
theories that admit a well-defined variational principle when the fields
satisfy boundary conditions on a timelike surface with corners. An interesting
feature of our analysis is that the fields are not required to be fully
on-shell.Comment: 51 page
The Electric Field at the Chargeless Interface Between Two Regions of Space
A common method for solving Poisson\u27s equation in electrostatics is to patch together two or more solutions of Laplace\u27s equation using boundary conditions on the potential and its gradient. Other methods may generate solutions without the need to check these conditions explicitly, and reconciling these solutions with the appropriate boundary conditions can be surprisingly subtle. As a result, a student may arrive at paradoxical conclusions—even in the case of elementary problems—that seem to be at odds with basic physical intuition. We illustrate this issue by showing how the potential of a uniformly charged ring appears to violate continuity of the normal component of the electric field at a chargeless surface
Conventions, Definitions, Identities, and Other Useful Formulae
As the name suggests, these notes contain a summary of important conventions, definitions, identities, and various formulas that I often refer to. They may prove useful for researchers working in General Relativity, Supergravity, String Theory, Cosmology, and related areas
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