Thermodynamics of boosted Schwarzschild black holes
The equilibrium thermodynamics of boosted Schwarzschild black holes is worked out in a concise way and shown to agree with expectations from relativistic thermodynamics.
gr-qc↗
arXiv subjects
Glenn Barnich
Publications and source records attributed to Glenn Barnich.
Memory of Robinson-Trautman waves
The memory effect for Robinson-Trautman waves is explicitly worked out. In a first step, we construct the combined frame rotation and coordinate transformation in which Robinson-Trautman waves are manifestly locally asymptotically flat at future null infinity. This allows us to apply well-established results on how to derive the memory effect in this context. In a second step, we construct a suitably improved generalized mass aspect that provides a local Lyapunov function for the flow in the sense that it is manifestly positive. News-free solutions are studied in detail and shown to coincide with the vacuum sector of Euclidean Liouville theory. They correspond to a boosted and rescaled Schwarzschild black hole. As a by-product, we show that the displacement and non-linear memory effects in locally asymptotically flat spacetimes at future null infinity are invariant under supertranslations and covariant under $\mathrm{BMS}_4$ Lorentz transformations and constant rescalings. A novel interpretation of modified flows that control the low harmonics in terms of keeping the system in its instantaneous rest frame is provided.
gr-qc↗
BV-BRST Noether theorem
The BRST Noether theorem, or ``Noether's 1.5 theorem'', asserts the triviality of the BRST Noether current. We provide two proofs of this theorem that are both valid without restriction on the structure of the gauge theory, extending thereby previous proofs holding in the case of gauge theories for which the solution of the master equation is linear in the antifields. We also relate explicitly the BRST Noether current to the BRST master current appearing in the master equation.
hep-th↗
Model spaces as constrained Hamiltonian systems: I. Application to $\mathrm{SU}(2)$
Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose that a central building block in the construction of the model space for a generic Lie group $G$ is the symplectic submanifold of $T^*G$ that one obtains when one imposes only the second class constraints in the construction of the coadjoint orbit as a symplectic quotient. Before turning to the non-compact infinite-dimensional groups relevant in the gravitational setting, we work out all details in the simplest case of $\mathrm{SU}(2)$. Besides recovering well-known results on the quantum theory of angular momentum from a unified perspective, the analysis sheds some light on the definition and properties of spin-weighted/monopole spherical harmonics.
hep-th↗
Modular properties of massive scalar partition functions
We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form $\mathbb R^{d-q}\times \mathbb T^{q+1}$ and show that they possess an ${\rm SL}(q+1,\mathbb Z)$ symmetry. Non-trivial relations between equivalent expressions for the result are obtained by doing the computation using functional, canonical and worldline methods. For $q=1$, the results exhibit modular symmetry and may be expressed in terms of massive Maass-Jacobi forms. In the complex case with chemical potential for ${\rm U}(1)$ charge turned on, the usual discussion of relativistic Bose-Einstein condensation is modified by the presence of the small dimensions.
hep-th↗
Chiral shift symmetries as an infinite tower of subleading super-shift symmetries
Chiral shift symmetries of the massless free bosons in two dimensions are global symmetries that are somewhat similar to asymptotic symmetries. They are most transparent in double-null coordinates where they are parametrized by two functions of one variable. In BMS-type coordinates, half of them appear as an infinite tower of sub-leading super-shift symmetries.
hep-th↗
Lessons from discrete light-cone quantization for physics at null infinity: Bosons in two dimensions
Motivated by issues in the context of asymptotically flat spacetimes at null infinity, we discuss in the simplest example of a massless scalar field in two dimensions several subtleties that arise when setting up the canonical formulation on a single or on two intersecting null hyperplanes with a special emphasis on the infinite-dimensional global and conformal symmetries and their canonical generators, the free data, a consistent treatment of zero modes, matching conditions, and implications for quantization of massless versus massive fields.
hep-th↗
Geometric action for extended Bondi-Metzner-Sachs group in four dimensions
The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS$_4$ generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS$_4$ Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evolution equations of non-radiative asymptotically flat spacetimes at null infinity.
hep-th↗
Phase transition of photons and gravitons in a Casimir box
A first order phase transition for photons and gravitons in a Casimir box is studied analytically from first principles with a detailed understanding of symmetry breaking due to the boundary conditions. It is closely related to Bose-Einstein condensation and accompanied by a quantum phase transition whose control parameter is the chemical potential for optical helicity.
hep-th↗
Notes on massless scalar field partition functions, modular invariance and Eisenstein series
The partition function of a massless scalar field on a Euclidean spacetime manifold $\mathbb{R}^{d-1}\times\mathbb{T}^2$ and with momentum operator in the compact spatial dimension coupled through a purely imaginary chemical potential is computed. It is modular covariant and admits a simple expression in terms of a real analytic SL$(2,\mathbb{Z})$ Eisenstein series with $s=(d+1)/2$. Different techniques for computing the partition function illustrate complementary aspects of the Eisenstein series: the functional approach gives its series representation, the operator approach yields its Fourier series, while the proper time/heat kernel/world-line approach shows that it is the Mellin transform of a Riemann theta function. High/low temperature duality is generalized to the case of a non-vanishing chemical potential. By clarifying the dependence of the partition function on the geometry of the torus, we discuss how modular covariance is a consequence of full SL$(2,\mathbb{Z})$ invariance. When the spacetime manifold is $\mathbb{R}^p\times\mathbb{T}^{q+1}$, the partition function is given in terms of a SL$(q+1,\mathbb{Z})$ Eisenstein series again with $s=(d+1)/2$. In this case, we obtain the high/low temperature duality through a suitably adapted dual parametrization of the lattice defining the torus. On $\mathbb{T}^{d+1}$, the computation is more subtle. An additional divergence leads to an harmonic anomaly.
hep-th↗
Coadjoint representation of the BMS group on celestial Riemann surfaces
The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane. The structure constants are worked out for different choices of bases. The conserved current algebra of non-radiative asymptotically flat spacetimes is explicitly interpreted in these terms.
gr-qc↗
Weyl Charges in Asymptotically Locally AdS$_3$ Spacetimes
We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS General Relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl abelian sector. The charges associated to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial central extension in the Weyl sector, related to the well-known Weyl anomaly. We then construct the holographic Weyl current and show that it satisfies an anomalous Ward-Takahashi identity of the boundary theory.
hep-th↗
Gravitons in a Casimir box
The partition function of gravitons with Casimir-type boundary conditions is worked out. The simplest box that allows one to achieve full analytical control consists of a slab geometry with two infinite parallel planes separated by a distance d. In this setting, linearized gravity, like electromagnetism, is equivalent to two free massless scalar fields, one with Dirichlet and one with Neumann boundary conditions, which in turn may be combined into a single massless scalar with periodic boundary conditions on an interval of length 2d. When turning on a chemical potential for suitably adapted spin angular momentum, the partition function is modular covariant and expressed in terms of an Eisenstein series. It coincides with that for photons. At high temperature, the result provides in closed form all subleading finite-size corrections to the standard (gravitational) black body result. More interesting is the low-temperature/small distance expansion where the leading contribution to the partition function is linear in inverse temperature and given in terms of the Casimir energy of the system, whereas the leading contribution to the entropy is proportional to the area and originates from gravitons propagating parallel to the plates.
hep-th↗
Modular invariance in finite temperature Casimir effect
The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell's theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.
hep-th↗
Conserved currents in the Palatini formulation of general relativity
We derive the expressions for the local, on-shell closed co-dimension 2 forms in the Palatini formulation of general relativity and explicitly show their on-shell equivalence to those of the metric formulation. When compared to other first order formulations, two subtleties have to be addressed during the construction: off-shell non-metricity and the fact that the transformation of the connection under infinitesimal diffeomorphisms involves second order derivatives of the associated vector fields.
gr-qc↗
BMS current algebra in the context of the Newman-Penrose formalism
Starting from an action principle adapted to the Newman-Penrose formalism, we provide a self-contained derivation of BMS current algebra, which includes the generalization of the Bondi mass loss formula to all BMS generators. In the spirit of the Newman-Penrose approach, infinitesimal diffeomorphisms are expressed in terms of four scalars rather than a vector field. In this framework, the on-shell closed co-dimension two forms of the linearized theory associated with Killing vectors of the background are constructed from a standard algorithm. The explicit expression for the breaking that occurs when using residual gauge transformations instead of exact Killing vectors is worked out and related to the presymplectic flux.
gr-qc↗
Soft degrees of freedom, Gibbons-Hawking contribution and entropy from Casimir effect
Recent work on non proper-gauge degrees of freedom in the context of the Casimir effect is reviewed. In his original paper, Casimir starts by pointing out that, when the electromagnetic field is confined between two perfectly conducting parallel plates, there is an additional physical polarization of the electromagnetic field at zero value for the discretized longitudinal momentum besides the standard two transverse polarizations at non-zero values. In this review, the dynamics of these additional modes is obtained from first principles. At finite temperature, their contribution to the entropy is proportional to the area of the plates and corresponds to the contribution of a massless scalar field in 2+1 dimensions. When the plates are charged, there is a further contribution to the partition function from the zero mode of this additional scalar that scales with the area but does not contribute to the entropy. It reproduces the result obtained when the Gibbons-Hawking method is applied to the vacuum capacitor. For completeness, a brief discussion of the classical thermodynamics of such a capacitor is included.
hep-th↗
Black hole entropy from non-proper gauge degrees of freedom: II. The charged vacuum capacitor
The question which degrees of freedom are responsible for the classical part of the Gibbons-Hawking entropy is addressed. A physical toy model sharing the same properties from the viewpoint of the linearized theory is a charged vacuum capacitor. In Maxwell's theory, the gauge sector including ghosts is a topological field theory. When computing the grand canonical partition function with a chemical potential for electric charge in the indefinite metric Hilbert space of the BRST quantized theory, the classical contribution originates from the part of the gauge sector that is no longer trivial due to the boundary conditions required by the physical set-up. More concretely, in the benchmark problem of a planar charged vacuum capacitor, we identify the degrees of freedom that, in the quantum theory, give rise to an additional contribution to the standard black body result proportional to the area of the plates, and that allow for a microscopic derivation of the thermodynamics of the charged capacitor.
hep-th↗