Classical and Thermodynamic Stability of Black Branes


## Jul 14, 2015

* Lorenz gauge: A gauge in which ∇ a A a = 0, or = (any g-valued function on spacetime), so ∇ 2 A a = J a; The residual freedom is A a $$\mapsto$$ A a + ∂ a χ, with ∇ 2 χ = 0, and can be used to impose the Coulomb gauge; Note: It is named after Ludwig Valentin Lorenz, and not after the Hendrik Antoon Lorentz of the Lorentz The recent starting of the gravitational wave (GW) astronomy with the events GW150914, GW151226, GW170104, and the very recent GW170814 and GW170817 seems to be fundamental not only in order to obtain new intriguing astrophysical information from our surrounding Universe, but also in order to discriminate among Einstein’s general theory of relativity (GTR) and alternative gravitational XII, we found that the transverse-traceless gauge gravitational wave emitted from a source was hTT ij= 1 R 2Q¨ +n kn lQ¨ klδ +n in jn n Q¨ −2n n Q¨ik −2n n Q¨jk . (19) We now want to know the eﬀective energy density in said gravitational waves far from the source. Using Eq. (18), and recalling that Qij is traceless, this is ht00i University of Pennsylvania ScholarlyCommons Department of Physics Papers Department of Physics 4-2-2012 Spatially Covariant Theories of a Transverse, Traceless Graviton: Formalism

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XII, we found that the transverse-traceless gauge gravitational wave emitted from a source was hTT ij= 1 R 2Q¨ +n kn lQ¨ klδ +n in jn n Q¨ −2n n Q¨ik −2n n Q¨jk . (19) We now want to know the eﬀective energy density in said gravitational waves far from the source. Using Eq. (18), and recalling that Qij is traceless, this is ht00i