Following Dirac's brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by varying the bulk coordinate system itself. Imposing appropriate Dirac style boundary conditions on the constrained 'sandwiched' gravitational action, we show how Israel junction conditions get relaxed, but remarkably, all solutions of the original Israel equations are still respected. The Israel junction conditions are traded, in the Z2-symmetric case, for a generalized Regge-Teitelboim type equation (plus a local conservation law), and in the generic Z2-asymmetric case, for a pair of coupled Regge-Teitelboim equations. The Randall-Sundrum model and its derivatives, such as the Dvali-Gabadadze-Porrati and the Collins-Holdom models, get generalized accordingly. Furthermore, Randall-Sundrum and Regge-Teitelboim brane theories appear now to be two different faces of the one and the same unified brane theory. Within the framework of unified brane cosmology, we examine the dark matter/energy interpretation of the effective energy/momentum deviations from General Relativity. I. INTRODUCTIONIn an almost forgotten paper [1] entitled "An extensible model of the electron", Dirac has made an attempt to picture a classical spinless electron as a breathing bubble in the electromagnetic field 'with no constraints fixing its size and shape'. Some positive surface tension has been invoked in order 'to prevent the electron from flying apart under the Coulomb repulsion of it surface charge'. On the practical side, this naive model has not made any impact on particle physics, so in this paper, we make no use of the model itself. On the field theoretical side, however, although gravity was switched off in this paper, it was nonetheless the first brane model. The equations of motion are derivable from an action principle, and in particular, the model offers a detailed prescription how to consistently perform brane variation. In the present paper, we switch on gravity, and apply the Dirac brane variation prescription to modern brane theories.Our main result is that the Israel[2] junction conditions (IJC), which are known to play a central role in all modern brane theories, get in fact relaxed. While every IJC solution is still strictly respected, it represents now a whole (continuous) family of new solutions. This opens the door for brane unification. To be more specific, as schematically illustrated in Fig.1 The Randall-Sundrum theory is very well known, and has rightly attracted lots of attention from General Relativity [7], cosmology [8] in particular, and also from string theory[9] points of view. See Ref.[10] for some brane world reviews, and Ref.[11] for some earlier brane models. The much older Regge-Teitelboim theory, on the other hand, a generalized Nambu-Goto type brane theory [3] for quantum gravity, has remained quite unfamiliar. This is partially due to the fact that the theory was o...
If general relativity is spontaneously induced, the black hole limit is governed by a phase transition which occurs precisely at the would have been horizon. The exterior Schwarzschild solution then connects with a novel core of vanishing spatial volume. The Kruskal structure, admitting the exact Hawking imaginary time periodicity, is recovered, with the conic defect defused at the origin, rather than at the horizon. The entropy stored inside any interior sphere is universal, equal to a quarter of its surface area, thus locally saturating the 't Hooft-Susskind holographic bound. The associated Komar mass and material energy functions are non-singular.Black hole thermodynamics is anchored to the well known Bekenstein-Hawking area entropy formula [1]. Intriguingly, neither the Gibbons-Hawking [2] Euclidean path integral derivation, nor the more locally oriented Wald's [3] derivation, make use of the black hole interior. This seems to tell us that aside from the singularity in its origin, the interior region of a black hole is quite a 'boring' place. Following this line, the area entropy has triggered the fascinating idea that, from some obscure reason, no physical degrees of freedom can reside within the interior of a black hole. If it is the case, these degrees of freedom, whatever they are, are owed to live on or near the horizon surface, with one bit of information per a quarter of Planck area [4]. The brane paradigm model, which introduces the notion of a stretched horizon [5], is a realization of this idea. The catch is, however, that the horizon looks perfectly innocent to in-falling matter. The apparent inconsistency between the horizon as a physical entity and as the mere point of no return has ignited a famous debate in the physical society. The black hole entropy formula has also inspired the so-called holographic principle [6]. The latter, primarily introduced by 't Hooft [7], attempting to resolve the black hole information paradox, and further developed by Susskind[8] to deal with black hole complementarity, is recently gaining theoretical support from the AdS/CFT duality [9].Apparently, as far as entropy packing is concerned, the interior of a black hole seems to be superfluous, certainly within the framework of general relativity per se. However, if general relativity is not a fundamental theory, but rather a spontaneously induced theory of gravity, the black hole limit has been shown [10] to be governed by a phase transition which occurs precisely at the would have been horizon. The fully recovered general relativistic exterior solution then connects with a novel core of vanishing spatial volume. The idea of horizon phase transition [11] is not new, and so is the notion of black stars and fuzzballs [12]. In this paper, after reviewing the fine details of the underlying phase transition geometry [10], we show how the black hole entropy is consistently packed inside the whole interior region. This is done in a universal manner, while locally saturating the 't Hooft-Susskind holographic bound, and is ...
We analyze, within the framework of unified brane gravity, the weak-field perturbations caused by the presence of matter on a 3-brane. Although deviating from the Randall-Sundrum approach, the masslessness of the graviton is still preserved. In particular, the four-dimensional Newton force law is recovered, but serendipitously, the corresponding Newton constant is shown to be necessarily lower than the one which governs FRW cosmology. This has the potential to puzzle out cosmological dark matter. A subsequent conjecture concerning galactic dark matter follows.
Current measurements of the γ-ray Fermi bubbles (FB) are based on model-dependent tracers, carry substantial systematic uncertainties, and are at some tension with each other. We show that gradient filters pick out the FB edges, which are found to smoothly connect to the bipolar X-ray structure emanating from the Galactic center, thus supporting the interpretation of the FBs as a Galacticscale phenomenon. The sharp edges facilitate a direct, model-free measurement of the peripheral FB spectrum. The result is strikingly similar to the full FB-integrated spectrum, softened by a power law of index η ≃ (0.2-0.3). This is naturally explained, in both hadronic and leptonic models, if cosmic rays are injected at the edge, and diffuse away preferentially at higher energies E. The inferred, averaged diffusion function in the (more plausible) leptonic model, D(E) ≃ 10 29.5 (E/10 GeV) 0.48±0.02 cm 2 s −1 , is consistent with estimates for Kraichnan-like turbulence. Our results, in particular the minute spatial variations in η, indicate that the FB edge is a strong, Mach 5, forward shock.
Hawking-Bekenstein entropy formula seems to tell us that no quantum degrees of freedom can reside in the interior of a black hole. We suggest that this is a consequence of the fact that the volume of any interior sphere of finite surface area simply vanishes. Obviously, this is not the case in general relativity. However, we show that such a phenomenon does occur in various gravitational theories which admit a spontaneously induced general relativity. In such theories, due to a phase transition (one parameter family degenerates) which takes place precisely at the would have been horizon, the recovered exterior Schwarzschild solution connects, by means of a self-similar transition profile, with a novel 'hollow' interior exhibiting a vanishing spatial volume and a locally varying Newton constant. This constitutes the so-called 'hollowgraphy' driven holography.
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