Conventions, Definitions, Identities, and Other Useful Formulae

As the name suggests, these notes contain a summary of important conventions, definitions, identities, and various formulas that I often refer to. They may prove useful for researchers working in General Relativity, Supergravity, String Theory, Cosmology, and related areas

Black holes in the conical ensemble

We consider black holes in an “unsuitable box”: a finite cavity coupled to a thermal reservoir at a temperature different than the black hole’s Hawking temperature. These black holes are described by metrics that are continuous but not differentiable due to a conical singularity at the horizon. We include them in the Euclidean path integral sum over configurations, and analyze the effect this has on black hole thermodynamics in the canonical ensemble. Black holes with a small deficit (or surplus) angle may have a smaller internal energy or larger density of states than the nearby smooth black hole, but they always have a larger free energy. Furthermore, we find that the ground state of the ensemble never possesses a conical singularity. When the ground state is a black hole, the contributions to the canonical partition function from configurations with a conical singularity are comparable to the contributions from smooth fluctuations of the fields around the black hole background. Our focus is on highly symmetric black holes that can be treated as solutions of two-dimensional dilaton gravity models: examples include Schwarzschild, asymptotically Anti-de Sitter, and stringy black holes

Bounds on extra dimensions from micro black holes in the context of the metastable Higgs vacuum

We estimate the rate at which collisions between ultrahigh-energy cosmic rays can form small black holes in models with extra dimensions. If recent conjectures about false vacuum decay catalyzed by black hole evaporation apply, the lack of vacuum decay events in our past light cone may place new bounds on the black hole formation rate and thus on the fundamental scale of gravity in these models. For theories with fundamental scale E∗ above the Higgs instability scale of the Standard Model, we find a lower bound on E∗ that is within about an order of magnitude of the energy where the cosmic-ray spectrum begins to show suppression from the Greisen-Zatsepin-Kuzmin effect. Otherwise, the abundant formation of semiclassical black holes with short lifetimes would likely initiate vacuum decay. Assuming a Higgs instability scale at the low end of the range compatible with experimental data, the excluded range is approximately 1017  eV≲E∗≤1018.8  eV for theories with n=1 extra dimension, narrowing to 1017  eV≲E∗≤1018.1  eV for n=6. These bounds rule out regions of parameter space that are inaccessible to collider experiments, small-scale gravity tests, or estimates of Kaluza-Klein processes in neutron stars and supernovae

Cosmological Constant as Confining U(1) Charge in Two-Dimensional Dilaton Gravity

The cosmological constant is treated as a thermodynamical parameter in the framework of two-dimensional dilaton gravity. We find that the cosmological constant behaves as a U(1) charge with a confining potential, and that such potentials require a novel Born-Infeld boundary term in the action. The free energy and other thermodynamical quantities of interest are derived, from first principles, in a way that is essentially model independent. We discover that there is always a Schottky anomaly in the specific heat and explain its physical origin. Finally, we apply these results to specific examples, like anti-de Sitter–Schwarzschild–Tangherlini black holes, Bañados-Teitelboim-Zanelli black holes and the Jackiw-Teitelboim model

The Interplay Between θ\theta and T

We extend a recent computation of the dependence of the free energy, F, on the noncommutative scale $\theta$ to theories with very different UV sensitivity. The temperature dependence of $F$ strongly suggests that a reduced number of degrees of freedom contributes to the free energy in the non-planar sector, $F_{\rm np}$, at high temperature. This phenomenon seems generic, independent of the UV sensitivity, and can be traced to modes whose thermal wavelengths become smaller than the noncommutativity scale. The temperature dependence of $F_{\rm np}$ can then be calculated at high temperature using classical statistical mechanics, without encountering a UV catastrophe even in large number of dimensions. This result is a telltale sign of the low number of degrees of freedom contributing to $F$ in the non-planar sector at high temperature. Such behavior is in marked contrast to what would happen in a field theory with a random set of higher derivative interactions.Comment: 14 pages, 1 eps figur

Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity

The on-shell gravitational action and the boundary stress tensor are essential ingredients in the study of black hole thermodynamics. We employ the Hamilton-Jacobi method to calculate the boundary counterterms necessary to remove the divergences and allow the study of the thermodynamics of Einstein-Gauss-Bonnet black holes.Comment: 21 pages, LaTe

Winding effects on brane/anti-brane pairs

We study a brane/anti-brane configuration which is separated along a compact direction by constructing a tachyon effective action which takes into account transverse scalars. Such an action is relevant in the study of HQCD model of Sakai and Sugimoto of chiral symmetry breaking, where the size of the compact circle sets the confinement scale. Our approach is motivated by string theory orbifold constructions and gives a route to model inhomogeneous tachyon decay. We illustrate the techniques involved with a relatively simple example of a harmonic oscillator on a circle. We will then repeat the analysis for the Sakai-Sugimoto model and show that by integrating out the winding modes will provide us with a renormalized action with a lower energy than that of truncating to zero winding sector.Comment: 21 pages, 3 figures. v3: discussion and references added, published versio

Thermodynamics of Black Holes in Two (and Higher) Dimensions

A comprehensive treatment of black hole thermodynamics in two-dimensional dilaton gravity is presented. We derive an improved action for these theories and construct the Euclidean path integral. An essentially unique boundary counterterm renders the improved action finite on-shell, and its variational properties guarantee that the path integral has a well-defined semi-classical limit. We give a detailed discussion of the canonical ensemble described by the Euclidean partition function, and examine various issues related to stability. Numerous examples are provided, including black hole backgrounds that appear in two dimensional solutions of string theory. We show that the Exact String Black Hole is one of the rare cases that admits a consistent thermodynamics without the need for an external thermal reservoir. Our approach can also be applied to certain higher-dimensional black holes, such as Schwarzschild-AdS, Reissner-Nordstrom, and BTZ.Comment: 63 pages, 3 pdf figures, v2: added reference

Black hole mass and Hamilton-Jacobi counterterms

We apply the method of holographic renormalization to computing black hole masses in asymptotically anti-de Sitter spaces. In particular, we demonstrate that the Hamilton-Jacobi approach to obtaining the boundary action yields a set of counterterms sufficient to render the masses finite for four, five, six and seven-dimensional R-charged black holes in gauged supergravities. In addition, we prove that the familiar black hole thermodynamical expression Ω = E−TS−ΦIQI continues to hold in general in the presence of arbitrary matter couplings to gravity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49158/2/jhep052005034.pd

Inhibition of Cholinergic Signaling Causes Apoptosis in Human Bronchioalveolar Carcinoma

Recent case-controlled clinical studies show that bronchioalveolar carcinomas (BAC) are correlated with smoking. Nicotine, the addictive component of cigarettes, accelerates cell proliferation through nicotinic acetylcholine receptors (nAChR). In this study, we show that human BACs produce acetylcholine (ACh) and contain several cholinergic factors including acetylcholinesterase (AChE), choline acetyltransferase (ChAT), choline transporter 1 (CHT1, SLC5A7), vesicular acetylcholine transporter (VAChT, SLC18A3), and nACh receptors (AChRs, CHRNAs). Nicotine increased the production of ACh in human BACs, and ACh acts as a growth factor for these cells. Nicotine-induced ACh production was mediated by α7-, α3β2-, and β3-nAChRs, ChAT and VAChT pathways. We observed that nicotine upregulated ChAT and VAChT. Therefore, we conjectured that VAChT antagonists, such as vesamicol, may suppress the growth of human BACs. Vesamicol induced potent apoptosis of human BACs in cell culture and nude mice models. Vesamicol did not have any effect on EGF or insulin-like growth factor-II–induced growth of human BACs. siRNA-mediated attenuation of VAChT reversed the apoptotic activity of vesamicol. We also observed that vesamicol inhibited Akt phosphorylation during cell death and that overexpression of constitutively active Akt reversed the apoptotic activity of vesamicol. Taken together, our results suggested that disruption of nicotine-induced cholinergic signaling by agents such as vesamicol may have applications in BAC therapy