3,091 research outputs found
Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
We develop an approach to the theory of relativistic geometric flows and
emergent gravity defined by entropy functionals and related statistical
thermodynamics models. Nonholonomic deformations of G. Perelman's functionals
and related entropic values are used for deriving relativistic geometric
evolution flow equations. For self-similar configurations, such equations
describe generalized Ricci solitons defining modified Einstein equations. We
analyze possible connections between relativistic models of nonholonomic Ricci
flows and emergent modified gravity theories. We prove that corresponding
systems of nonlinear partial differential equations, PDEs, for entropic flows
and modified gravity possess certain general decoupling and integration
properties. There are constructed new classes of exact and parametric solutions
for nonstationary configurations and locally anisotropic cosmological metrics
in modified gravity theories and general relativity. Such solutions describe
scenarios of nonlinear geometric evolution and gravitational and matter field
dynamics with pattern-forming and quasiperiodic structure and various space
quasicrystal and deformed spacetime crystal models. We analyze new classes of
generic off-diagonal solutions for entropic gravity theories and show how such
solutions can be used for explaining structure formation in modern cosmology.
Finally, we speculate why the approaches with Perelman-Lyapunov type
functionals are more general or complementary to the constructions elaborated
using the concept of Bekenstein-Hawking entropy.Comment: accepted to EPJC; latex2e 11pt, 35 pages with a table of contents; v3
is substantially modified with a new title and a new co-autho
Ultraspinning limits and rotating hyperboloid membranes
We apply the hyperboloid membrane limit to the general Kerr-AdS metrics and
their recently studied super-entropic cousins and obtain a new class of
rotating black holes, for which the rotational parameters in multiple
directions attain their maximal value---equal to the AdS radius. These new
solutions have a potential application in the description of holographic fluids
with vorticity. They also possess interesting thermodynamic properties: we show
that---despite the absence of Misner strings---the Bekenstein--Hawking
entropy/area law is still violated, raising a question about the origin of this
violation.Comment: 10 pages, 2 figures, REVTeX 4-
Entropic force and its fluctuation in Euclidian quantum gravity
In this paper, we study the idea about gravity as entropic force proposed by
Verlinde. By applying the identification between partition functions of gravity
theory and the dual field theory, we find the gravitational force can be
calculated from the changing of entropy induced from its dual field theory
side. Unlike Verlinde's calculation, our method does not depend on other
assumptions such as equipartition of energy, so it is a safe check on the
entropic force idea. Also we show how entropic force can be derived by similar
method from gravity side along, which will provide a clue to a better
understanding on the gauge/gravity duality. At last, we study the fluctuation
of the force, and we find the fluctuation acting on the point-like particle can
never be larger than the expectation value of the force. For black hole in AdS
space, by gauge/gravity duality, the fluctuation is induced by thermal
fluctuation from field theory living on conformal boundary. And for the metric
of black hole in flat space, the ratio between fluctuation and force goes to a
constant at infinity. .Comment: typos revised, more detailed discussio
Thermodynamic Metrics and Black Hole Physics
We give a brief survey of thermodynamic metrics, in particular the Hessian of
the entropy function, and how they apply to black hole thermodynamics. We then
provide a detailed discussion of the Gibbs surface of Kerr black holes. In
particular we analyze its global properties, and extend it to take the entropy
of the inner horizon into account. A brief discussion of Kerr-Newman black
holes is included.Comment: 21 pages, new figures adde
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