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Register a new userWeyl anomalies and the nature of the gravitational field
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The presence of gravity generalizes the notion of scale invariance to Weyl invariance, namely, invariance under local rescalings of the metric. In this work, we have computed the Weyl anomaly for various classically scale or Weyl invariant theories, making particular emphasis on the differences that arise when gravity is taken as a dynamical fluctuation instead of as a non-dynamical background field. We find that the value of the anomaly for the Weyl invariant coupling of scalar fields to gravity is sensitive to the dynamical character of the gravitational field, even when computed in constant curvature backgrounds. We also discuss to what extent those effects are potentially observable.
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Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is available. It is found that the total energy emitted from the horizon for the electromagnetic field is just (d-2) times as that for a scalar field. The results support the picture that Hawking radiation can be regarded as an anomaly eliminator on horizons. Possible extensions and applications of the analysis are discussed.
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with appropriate fall-off for the matter fields, admit a degenerate Maxwell field that squares to give the Weyl tensor. The converse statement also holds, i.e. if there exists a degenerate Maxwell field on a curved background, then the background is type N. This relation defines a scalar that satisfies the wave equation on the background. We show that for non-twisting radiative solutions, the Maxwell field and the scalar also satisfy the Maxwell equation and the wave equation on Minkowski spacetime. Hence, non-twisting solutions have a straightforward double copy interpretation.
Hairy black holes in the gravitational decoupling setup are studied from the perspective of conformal anomalies. Fluctuations of decoupled sources can be computed by measuring the way the trace anomaly-to-holographic Weyl anomaly ratio differs from unit. Therefore the gravitational decoupling parameter governing three hairy black hole metrics is then bounded to a range wherein one can reliably emulate AdS/CFT with gravitational decoupled solutions, in the tensor vacuum regime.
We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal. To fix the ambiguity inherent in the Wald-Zoupas definition of quasilocal charges, we propose a new principle, based on holographic reasoning, that the flux be of Dirichlet form. This also produces an expression for the analog of the Brown-York stress tensor on the null surface. Defining the algebra of charges using the Barnich-Troessaert bracket for open subsystems, we give a general formula for the central -- or more generally, abelian -- extensions that appear in terms of the anomalous transformation of the boundary term in the gravitational action. This anomaly arises from having fixed a frame for the null normal, and we draw parallels between it and the holographic Weyl anomaly that occurs in AdS/CFT. As an application of this formalism, we analyze the near-horizon Virasoro symmetry considered by Haco, Hawking, Perry, and Strominger, and perform a systematic derivation of the fluxes and central charges. Applying the Cardy formula to the result yields an entropy that is twice the Bekenstein-Hawking entropy of the horizon. Motivated by the extended Hilbert space construction, we interpret this in terms of a pair of entangled CFTs associated with edge modes on either side of the bifurcation surface.
I review a string-inspired cosmological model with gravitational anomalies in its early epochs, which is based on fields from the (bosonic) massless gravitational multiplet of strings, in particular gravitons and Kalb Ramond (KR), string-model independent, axions (the dilaton is assumed constant). I show how condensation of primordial gravitational waves, which are generared at the very early eras immediately after the big bang, can lead to inflation of the so called running vacuum model (RVM) type, without external inflatons. The role of the slow-roll field is played by the KR axion, but it does not drive inflation. The non-linearities in the anomaly terms do. Chiral fermionic matter excitations appear at the end of this RVM inflation, as a result of the decay of the RVM vacuum, and are held responsible for the cancellation of the primordial gravitational anomalies. Chiral anomalies, however, survive in the post-inflationary epochs, and can lead to the generation of a non perturbative mass for the KR axion, which could thus play the role of dark matter in this Universe. As a result of the condensed gravitational anomaly, there is a Lorentz-invariance violating KR axion background, which remains undiluted during the RVM inflation, and can lead to baryogenesis through leptogenesis in the radiation era, in models with sterile right-handed neutrinos. I also discuss the phenomenology of the model in the modern era, paying particular attention to linking it with a version of RVM, called type II RVM, which arguably can alleviate observed tensions in the current-epoch cosmological data.
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