Shall Bekenstein's Area Law Prevail?

According to Bekenstein's area law, the black hole entropy is identified holographically - with one quarter of the horizon area. However, it is commonly believed that such a law is only valid in Einstein's theory and that higher curvature corrections generically give rise to its modifications. This is for example the case of black holes in Lovelock gravities, or their four-dimensional cousins in the recently discovered 4D scalar-tensor Gauss-Bonnet gravity where one naively 'finds' (classical) logarithmic corrections to the Bekenstein's law. In this note we argue that such logarithmic corrections originate from ignoring the shift symmetry of the 4D Gauss-Bonnet gravity. When this symmetry is properly taken into account, there is no longer any departure from the area law in this theory. Moreover, the first law remains valid upon modifying the black hole temperature, which can be derived via the Brown-York procedure but is no longer given by the surface gravity. Interestingly, we show that upon similar modification of the black hole temperature the area law can also prevail for black holes in higher-dimensional Lovelock gravities.Comment: 7 pages. Added appendix on recovering modified temperature via Brown-York procedure. Comments welcom

Quantum phenomenological gravitational dynamics: A general view from thermodynamics of spacetime

In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity modifications to it. Quantum gravity effects are considered via modification of Bekenstein entropy by an extra logarithmic term in the area. This modification is predicted by several approaches to quantum gravity, including loop quantum gravity, string theory, AdS/CFT correspondence and generalised uncertainty principle phenomenology, giving our result a general character. The derived equations generalise classical equations of motion of unimodular gravity, instead of the ones of general relativity, and they contain at most second derivatives of the metric. We provide two independent derivations of the equations based on thermodynamics of local causal diamonds. First one uses Jacobson's maximal vacuum entanglement hypothesis, the second one Clausius entropy flux. Furthermore, we consider questions of diffeomorphism and local Lorentz invariance of the resulting dynamics and discuss its application to a simple cosmological model, finding a resolution of the classical singularity.Comment: Extended discussions, extra references added. 31 pages, 1 figur

Emergence of quadratic gravity from entanglement equilibrium

In this work, we derive the linearised equations of quadratic gravity from entanglement equilibrium of local causal diamonds. Rather than starting from the Wald entropy prescription (which depends on the gravitational Lagrangian), we employ a model independent approach based on the logarithmic corrections to horizon entanglement entropy. In this way, we are able to show the emergence of linearised quadratic gravity from entanglement equilibrium without using any a priori knowledge about gravitational dynamics. If the logarithmic correction to entropy has a negative sign, as predicted by replica trick calculations of entanglement entropy, we find that the quadratic gravity correction terms have the sign necessary to avoid tachyonic instabilities of the theory.Comment: 8 pages, 1 figure. Matches the version accepted in PR

New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies

We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynamics implied by thermodynamics of spacetime, in fact, corresponds to unimodular gravity rather than general relativity.Comment: 19 pages, 1 figure Version accepted in PRD. Few typos corrected and some references adde

Thermodynamics of spacetime and unimodular gravity

In this review we discuss emergence of unimodular gravity (or, more precisely, Weyl transverse gravity) from thermodynamics of spacetime. By analyzing three different ways to obtain gravitational equations of motion by thermodynamic arguments, we show that the results point to unimodular rather than fully diffeomorphism invariant theories and that this is true even for modified gravity. The unimodular character of dynamics is especially evident from the status of cosmological constant and energy-momentum conservation.Comment: 16 pages, 2 figures. Review prepared for a Special Issue of the International Journal of Geometric Methods in Modern Physics dedicated to the conference Geometric Foundations of Gravity 202

Termodynamika černých děr. Entropie a informace.

Cílem této práce je poskytnout přehled problematiky termodynamiky černých děr a jejího vztahu ke konceptům entropie a fyzikální informace. Začneme odvozením čtyř zákonů termodynamiky černých děr v kontextu klasické obecné relativity. Následně pomocí semiklasické limity kvantové mechaniky ukážeme, že černé díry vyzařují a mají nenulovou termodynamickou teplotu. Druhá část práce je věnována zavedení Shannonovy a von Neumannovy entropie a fyzikální informace. Nakonec budeme diskutovat použití těchto konceptů v kontextu mechaniky černých děr. 1The aim of the thesis is to provide a review of black hole thermodynamics and its relation with concepts of entropy and physical information. We start by deriving the four laws of black hole thermodynamics in the context of classical general relativity. To supplement this, we use semiclassical limit of quantum mechanics to show that black holes radiate and have non-zero thermodynamic temperature. In the second part of the thesis we describe the concepts of the Shannon and von Neumann entropy and of physical information. Lastly, we discuss the use of these concepts in the context of black hole mechanics. 1Ústav teoretické fyzikyInstitute of Theoretical PhysicsMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Possibilities of determination of the correlation relations for the strength characteristics of shotcrete

Diplomová práce je zaměřena na možnosti stanovení korelačních vztahů pro pevnostní charakteristiky stříkaných betonů. Cílem diplomové práce je studium základních vlastností jednotlivých receptur stříkaných betonů. Důležitým bodem diplomové práce bude porovnání betonů vyrobených nástřikem s betony vyrobenými laboratorně s přítlakem. Na základě dosažených výsledků budou sestaveny korelační vztahy pro daný soubor betonů.The thesis is focused on the possibility of establishing correlation relationships for the strength characteristics of sprayed concrete. The aim of the thesis is to study the fundamental properties of sprayed concrete recipes. An important point of the thesis will bemade by spraying concrete compared with concrete made with laboratory pressure. Based on the achieved results will be compiled correlation equations for a given set of concrete.

Sales Promotion and Advertising of Company

Hlavním cílem mé práce je na základě provedených analýz navrhnout vhodné změny/doplnění marketingově komunikačních nástrojů konkrétní společnosti se zaměřením zejména na nástroje podpory prodeje a reklamu. Realizací návrhů by pak mělo dojít k navýšení povědomí o společnosti, získání nových zákazníků či zvýšení spokojenosti (a tím opětovné návštěvnosti) stávajících zákazníků. Také se chci zaměřit na nastoupení a následný chod podniku ve spojení s pandemickou situací a z toho vycházející krizí. První část teoretická je zaměřena na definování jednotlivých ekonomických pojmů, metod a nástrojů komunikace. Druhá část praktická, je hlavně založena na metodě analýzy současného stavu podniku a konkurence. V této části se také zaměřuji zejména na komunikační nástroje využívané salonem, dále na cílovou skupinu zákazníků, a celkové vyhodnocení.The main goal of my work is based on the analysis to propose appropriate changes / additions to marketing communication tools of a particular company, focusing mainly on sales promotion tools and advertising. The implementation of the proposals should then increase the awareness of the company, gain new customers or increase the satisfaction (and thus re-visit) of existing customers. I also want to focus on the start-up and subsequent operation of the company in connection with the pandemic situation and the resulting crisis. The first theoretical part is focused on defining individual economic concepts, methods and tools of communication. The second practical part is mainly based on the method of analysis of the current state of the company and the competition. In this part, I also focus mainly on the communication tools used by the salon, on the target group of customers, and the overall evaluation.