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Mu-in Park

Publications and source records attributed to Mu-in Park.

15 recordsLinked to original sources
arXiv2011

Horava Gravity and Gravitons at a Conformal Point

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. Here, I study the Horava model at $λ=1/3$, where an anisotropic Weyl symmetry exists in the UV limit, in addition to the foliation-preserving diffeomorphism. By considering linear perturbations around Minkowski vacuum, I show that the scalar graviton mode is completely disappeared and only the usual tensor graviton modes remain in the physical spectrum. The existence of the UV conformal symmetry is unique to the theory with the detailed balance and it is quite probable that $λ=1/3$ be the UV fixed point. This situation is analogous to $λ=1$, which is Lorentz invariant in the IR limit and is believed to be the IR fixed point.

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arXiv2010

Remarks on the Scalar Graviton Decoupling and Consistency of Horava Gravity

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. But there have been confusions regarding the extra scalar graviton mode and the consistency of the Horava model. I reconsider these problems and show that, in the Minkowski vacuum background, the scalar graviton mode can be consistency decoupled from the usual tensor graviton modes by imposing the (local) Hamiltonian as well as the momentum constraints.

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arXiv2009

A Test of Horava Gravity: The Dark Energy

Recently Horava proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I consider a non-trivial test of the new gravity theory in FRW universe by considering an IR modification which breaks "softly" the detailed balance condition in the original Horava model. I separate the dark energy parts from the usual Einstein gravity parts in the Friedman equations and obtain the formula of the equations of state parameter. The IR modified Horava gravity seems to be consistent with the current observational data but we need some more refined data sets to see whether the theory is really consistent with our universe. From the consistency of our theory, I obtain some constraints on the allowed values of w_0 and w_a in the Chevallier, Polarski, and Linder's parametrization and this may be tested in the near future, by sharpening the data sets.

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arXiv2009

Smeared Hairs and Black Holes in Three-Dimensional de Sitter Spacetime

It is known that there is no three-dimensional analog of de Sitter black holes. I show that the analog does exist when non-Gaussian (i.e., ring-type) smearings of point matter hairs are considered. This provides a new way of constructing black hole solutions from hairs. I find that the obtained black hole solutions are quite different from the usual large black holes in that there are i) large to small black hole transitions which may be considered as inverse Hawking-Page transitions and ii) soliton-like (i.e., non-perturbative) behaviors. For Gaussian smearing, there is no black hole but a gravastar solution exists.

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arXiv2009

The Black Hole and Cosmological Solutions in IR modified Horava Gravity

Recently Horava proposed a renormalizable gravity theory in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I study an IR modification which breaks "softly" the detailed balance condition in Horava model and allows the asymptotically flat limit as well. I obtain the black hole and cosmological solutions for "arbitrary" cosmological constant that represent the analogs of the standard Schwartzschild-(A)dS solutions which can be asymptotically (A)dS as well as flat and I discuss some thermodynamical properties. I also obtain solutions for FRW metric with an arbitrary cosmological constant. I study its implication to the dark energy and find that it seems to be consistent with current observational data.

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arXiv2009

Statistical Mechanics of Three-dimensional Kerr-de Sitter Space

The statistical computation of the (2+1)-dimensional Kerr-de Sitter space in the context of the {\it classical} Virasoro algebra for an asymptotic isometry group has been a mystery since first, the degeneracy of the states has the right value only at the infinite boundary which is casually disconnected from our universe, second, the analyses were based on the unproven Cardy's formula for complex central charge and conformal weight. In this paper, I consider the entropy in Carlip's "would-be gauge" degrees of freedom approach instead. I find that it agree with the Bekenstein-Hawking entropy but there are no the above problems. Implications to the dS/CFT are noted.

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arXiv2008

Constraint Dynamics and Gravitons in Three Dimensions

The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From counting the number of first and second class constraints, the number of dynamical degrees of freedom, which equals to the number of propagating graviton modes, is found to be 1, "regardless of" the value of cosmological constant. I note also that the usual equivalence with Chern-Simons gauge theory does "not" work for general circumstances.

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arXiv2008

Holography in Three-dimensional Kerr-de Sitter Space with a Gravitational Chern-Simons Term

The holographic description of the three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy-momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the usual Hawking temperature, and it is found that the usual Gibbons-Hawking entropy is modified. It is remarked that, due to the gravitational Chern-Simons term, (a) the results go beyond analytic continuation from AdS, (b) the maximum-mass/N-bound conjecture may be violated, and (c) the three-dimensional cosmology is chiral. A statistical mechanical computation of the entropy, from a Cardy-like formula for a dual CFT at the asymptotic boundary, is discussed. Some technical difference in the Chern-Simons energy-momentum tensor, from literatures is remarked also.

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arXiv2008

BTZ Black Hole with Higher Derivatives, the Second Law of Thermodynamics, and Statistical Entropy: A New Proposal

I consider the thermodynamics of the BTZ black hole in the presence of the higher curvature and gravitational Chern-Simons terms, and its statistical entropy. I propose a new thermodynamical entropy, which being {\it non-negative} manifestly, such as the second law, as well as the first law, of thermodynamics is satisfied. I show that the new \therl entropy agrees perfectly with the statistical entropy for $all$ the values of the conformal factor of the higher curvature terms and the coupling constant of the gravitational Chern-Simons term, in contrast to some disagreements in the literatures. The agreement with both the higher curvature and gravitational Chern-Simons terms is possible because of an appropriate balancing of them, though it is not a trivial matter because of a conflict in the appropriate Hilbert space for a well-defined conformal field theory for each term.

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arXiv2008

Can Hawking temperatures be negative ?

It has been widely believed that the Hawking temperature for a black hole is $uniquely$ determined by its metric and $positive$. But, I find that this does ``not'' seem to be true in the recently discovered black holes which include the exotic black holes and the black holes in the three-dimensional higher curvature gravities. I show that the Hawking temperatures, which are measured by the quantum fields in thermal equilibrium with the black holes, are $not$ the usual Hawking temperature but the $new$ temperatures that have been proposed recently and can be $negative$. The associated new entropy formulae, which are defined by the first law of thermodynamics, versus the black hole masses show some genuine effects of the black holes which do not occur in the spin systems. Some cosmological implications and physical origin of the discrepancy with the standard analysis are noted also.

hep-th↗
arXiv2008

Notes on the Area Theorem

Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes $positive$ energy matter, ``independent of the details of the gravity action''. I use this process to study the dynamics of the ``inner'' as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon ``can decrease'', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon ``never decrease'' such as the usual area theorem still works in our examples, though this is quite non-trivial in general. There exist the instability of the inner horizons and the connected effects of ``mass inflation'' but, according to more detailed analysis, it seems that the instability is not important in my analysis. I also find a ``generalized'' area theorem by combining those of the outer and inner horizons.

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arXiv2007

BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy

Recently, the BTZ black hole in the presence of the gravitational Chern-Simons (GCS) term has been studied and it has been found that the usual thermodynamical quantities, like as the black hole mass, angular momentum, and black hole entropy, are modified. But, for large values of the GCS coupling, where the modification terms dominate the original terms, some exotic behaviors occur, like as the roles of the mass and angular momentum are interchanged and the black hole entropy depends more on the $inner$-horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking (BH) entropy. Moreover, this entropy does $not$ agree with the statistical entropy, in contrast to a good agreement for small values of the GCS coupling. Here I find that there is another entropy formula where the usual BH form dominates the inner-horizon term again, as in the small GCS coupling, such as the second law of thermodynamics can be guaranteed. I compare the result of the holographic approach with the classical- symmetry-algebra-based approach and I find exact agreements even with the higher-derivative term of GCS. This provides a non-trivial check of the AdS/CFT-correspondence in the presence of higher-derivative terms in the gravity action.

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arXiv2007

The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length

Recently, the Heisenberg's uncertainty principle has been extended to incorporate the existence of a large (cut-off) length scale in de Sitter or anti-de Sitter space, and the Hawking temperatures of the Schwarzshild-(anti) de Sitter black holes have been reproduced by using the extended uncertainty principle. I generalize the extended uncertainty to the case with an absolute minimum length and compute its modification to the Hawking temperature. I obtain a general trend that the generalized uncertainty principle due to the absolute minimum length ``always'' increases the Hawking temperature, implying ``faster'' decay, which is in conformity with the result in the asymptotically flat space. I also revisit the ``black hole-string'' phase transition, in the context of the generalized uncertainty principle.

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arXiv2002

The Hamiltonian Dynamics of Bounded Spacetime and Black Hole Entropy: The Canonical Method

From first principles, I present a concrete realization of Carlip's idea on the black hole entropy from the conformal field theory on the horizon in any dimension. New formulation is free of inconsistencies encountered in Carlip's. By considering a correct gravity action, whose variational principle is well defined at the horizon, I $derive$ a correct $classical$ Virasoro generator for the surface deformations at the horizon through the canonical method. The existence of the classical Virasoro algebra is crucial in obtaining an operator Virasoro algebra, through canonical quantization, which produce the right central charge and conformal weight $\sim A_+/\hbar G$ for the semiclassical black hole entropy. The coefficient of proportionality depends on the choice of ground state, which has to be put in by hand to obtain the correct numerical factor 1/4 of the Bekenstein-Hawking (BH) entropy. The appropriate ground state is different for the rotating and the non-rotating black holes but otherwise it has a $universality$ for a wide variety of black holes. As a byproduct of my results, I am led to conjecture that {\it non-commutativity of taking the limit to go to the horizon and computing variation is proportional to the Hamiltonian and momentum constraints}. It is shown that almost all the known uncharged black hole solutions satisfy the conditions for the universal entropy formula.

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