einstein hilbert action and general relativity in vacuo

... of Inequality in Tax Policy,” January 21-22, 1999 in Washington, D.C. I am grateful to Christopher Taber for help in conducting the tax simulations, and to Jeffrey Smith for help in analyzing ... surprising and disappointing. In this essay, I question this criterion. Its anonymity postulates do not describe actual social decision making in which individuals evaluate oliies by asking whether ... the extensive margin (schooling) and at the intensive margin (hours of job training). Differences in ability are documented to affect the outcomes of human capital decisions in important ways.

Ngày tải lên: 18/02/2014, 01:20

... x 2 [...]... = r sin x1 sin x2 cos x3 … yn-1 = r sin x1 sin x2 sin x3 sin x4 … cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 … sin xn-1 cos xn yn+1 = r sin x1 sin x2 sin x3 sin x4 … sin xn-1 sin xn (d) ... x 3 … y n-1 = sin x 1 sin x 2 sin x 3 sin x 4 … cos x n-1 y n = sin x 1 sin x 2 sin x 3 sin x 4 … sin x n-1 cos x n y n+1 = sin x 1 sin x 2 sin x 3 sin x 4 … sin x n-1 sin x n In the ... Comoving Frames and Proper Time 94 12. The Stress Tensor and the Relativistic Stress-Energy Tensor 100 13. Two Basic Premises of General Relativity 109 14. The Einstein Field Equations and Derivation

Ngày tải lên: 17/03/2014, 14:28

... -r sin x 1 sin x 2 sin x 3 , r sin x 1 sin x 2 cos x 3 cos x 4 . . . , r sin x 1 sin x 2 cos x 3 sin x 4 … sin x n-1 cos x n , r sin x 1 sin x 2 cos x 3 sin x 4 … sin x n-1 sin ... cos x 1 sin x 2 … sin x n-1 sin x n ) ∂ ∂x 2 = (0, -r sin x 1 sin x 2 , . . . , r sin x 1 cos x 2 sin x 3 … sin x n-1 cos x n , r sin x 1 cos x 2 sin x 3 … sin x n-1 sin x n ). ∂ ... followihg generalized polar coordinates. y 1 = r cos x 1 y 2 = r sin x 1 cos x 2 y 3 = r sin x 1 sin x 2 cos x 3 … y n-1 = r sin x 1 sin x 2 sin x 3 sin x 4 … cos x n-1 y n = r sin x 1 sin

Ngày tải lên: 12/08/2014, 16:20

... 2 sin 2 x 1 sin 2 x 2 … sin 2 x n-1 g ij = 0 if i ≠ j so that g ** =         r 2 00… 0 0r 2 sin 2 x 1 0 … 0 00r 2 sin 2 x 1 sin 2 x 2 … 0 …… … … … 00 0 … r 2 sin 2 x 1 sin ... (“timelike”). Definition 6.4 If C is a non-null path in M, then define its length as follows: Break the path into segments S each of which lie in some coordinate neighborhood, and define the length ... (measuring time). Let us postulate that we are living in some kind of 4-dimensional manifold M (since we want to include time as a coordinate. By the way, we refer to a chart x at the point p

Ngày tải lên: 12/08/2014, 16:20

... constructed by bouncing a single photon back and forth bewtwwen two parallel mirrors as shown in in the following figure. 1 meter tick tock Now place this clock in a train moving in the x-direction ... v. By comparing the time it takes between a tick and a tock for a stationary observer and one on the train, obtain the time contraction formula (∆t– in terms ∆t) from the length contraction one. ... 2  00- ∫c 1-∫ 2  0100 0010 - ∫/c 1-∫ 2 00  1 1-∫ 2  . and hence the new coordinates (by integrating everything in sight; using the boundary conditions x– i = 0 when x i = 0) as 54 x–

Ngày tải lên: 12/08/2014, 16:20

... comoving reference frame; it is inertial at each point along our world line, but the direction of the axes are constantly changing in space-time. Proposition 9.6 (Changing Inertial Frames) If x and ... Answer Yes. At each instant in time, we can construct a local inertial frame corresponding to that event. But this frame varies from point to point along our world line if our world line is not a geodesic ... degrees of freedom in choosing local coordinates to be in an inertial frame. Three of these correspond to changing the coordinates by a constant velocity (3 degrees of freedom) or rotating about some

Ngày tải lên: 12/08/2014, 16:20

... the index by defining R abcd = g bi R a i cd Substituting the first of the above (boxed) formulas into the second, and using symmetry of the second derivatives and the metric tensor, we find ... corresponding to each point on the path. This (moving) coordinate system is called the momentary comoving frame of reference and corresponds to the “real life” coordinate systems. (c) Proper Coordinates ... dt dt (since t goes from 0 to 1 in C 1 ) = X j (a) - ⌡ ⌠ 0 1 ¶ i j 1 X i ©rdt . (using the definition of C 1 above) Warning: The integrand term ¶ i j 1 X i is not constant, and must be

Ngày tải lên: 12/08/2014, 16:20

... “straight line,” since that concept has no meaning in M; what's straight in the eyes of one chart is curved in the eyes of another. “Geodesic,” on the other hand, does make sense, since it is independent ... the other axes might be “spinning” about the path—it is hard to prescribe directions for the remaining axes in a convoluted twisting path. However, since we are using a small solid object, we ... law combines both energy conservation and momentum conservation into a single elegant law. Exercise Set 12 1. If aa aa , bb bb , and cc cc are any three vector fields in locally Minkowskain 4-manifold,

Ngày tải lên: 12/08/2014, 16:20

... metric tensor that would result in an inverse square repelling force (“antigravity”). 14. The Einstein Field Equations and Derivation of Newton's Law Einstein& apos;s field equations show ... defeat the purpose to choose an inertial frame. 103 (Here and in what follows, we are ignoring terms of order O(˙ 2 ).) Substituting this information in (II), and using the fact that P i ,4 = ... are not in an inertial frame (modulo scaling) since ˙ need not be constant, but we are in a frame that is almost inertial. 2. The metric g ** is obtained from the Minkowski g by adding a small

Ngày tải lên: 12/08/2014, 16:20

... large to begin with (big stars) this vicious cycle diverges, ending in the gravitational collapse of a star, leading to neutron stars or, in extreme cases, black holes. (b) Einstein Field Equations ... overwhelming even the quantum mechanical forces. In fact, it collapses to a singularity, a point with infinite density and no physical dimension, a black hole. For such objects, we have two distinct ... of the second and third terms in parentheses is skew-symmetric in r and k, whereas the term outside is symmetric in them. This results in them canceling when we sum over repeated indices. Thus,

Ngày tải lên: 12/08/2014, 16:20

... no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated In the interest ... emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects ... which points at rest remain at rest and points in motion continue permanently in uniform rectilinear motion As reference−body let us imagine a spacious chest resembling a room with an observer inside...

Ngày tải lên: 05/06/2014, 10:58

... is the high point of the course from the theoretical point of view We discuss Einstein s general theory of relativity from the point of view of the Einstein- Hilbert functional In fact we borrow ... title of Hilbert s paper for the Chapter heading We also introduce the principle of general covariance, first introduce by Einstein, Infeld, and Hoffmann to derive the “geodesic principle” and give ... the normal vector to point out of the cylinder or into the cylinder Of course, in the inward pointing case, the curvature has the opposite sign, k = −1/r For inward pointing normals, the formula...

Ngày tải lên: 17/03/2014, 14:28

... r sin x1 cos x2 sin x3 sin xn-1 sin xn) 3 = (0, 0, -r sin x sin x sin x , r sin x sin x cos x cos x , x r sin x1 sin x2 cos x3 sin x4 sin xn-1 cos xn, r sin x1 sin x2 cos x3 sin x4 sin ... getting y1 = r cos x y2 = r sin x1 cos x2 y3 = r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = r sin x1 sin x2 sin ... followihg generalized polar coordinates y1 = r cos x y2 = r sin x1 cos x2 y3 = r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1...

Ngày tải lên: 27/03/2014, 11:52

... sin x1 cos x2 sin x3 sin xn-1 sin xn) 42 3 = (0, 0, -r sin x sin x sin x , r sin x sin x cos x cos x , x r sin x1 sin x2 cos x3 sin x4 sin xn-1 cos xn, r sin x1 sin x2 cos x3 sin x4 sin ... getting y1 = r cos x1 y2 = r sin x1 cos x2 10 y3 = r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1 cos xn yn+1 = r sin x1 sin ... followihg generalized polar coordinates y1 = r cos x1 y2 = r sin x1 cos x2 y3 = r sin x1 sin x2 cos x3 yn-1 = r sin x1 sin x2 sin x3 sin x4 cos xn-1 yn = r sin x1 sin x2 sin x3 sin x4 sin xn-1...

Ngày tải lên: 24/04/2014, 17:08

... leading to insulin resistance Candidate genes involved in the mechanisms of insulin resistance Insulin signalling network Factors leading to insulin resistance Defining the function of the insulin ... analysis and alanine scanning (as reviewed in 9, 15 and 16) Four distinct binding epitopes have been identified, within the L1, CR, L2 and Fn1 insert domains Residues in the L1 and L2 domains of ... calcium/lipid-dependent protein kinase C, and as a homologue of a viral transforming protein v-Akt An important 26 THE INSULIN RECEPTOR AND DOWNSTREAM SIGNALLING breakthrough in understanding insulin signalling was...

Ngày tải lên: 09/08/2014, 15:20

... mixed muscle protein, myosin heavy chain and mitochondrial protein were unchanged in diabetic patients infused with insulin.120 It is interesting that intensive insulin treatment in type diabetic ... Figure 5.1 Insulin signalling pathways PROTEIN SYNTHESIS INSULIN SIGNALLING AND GLOBAL KNOCKOUTS 5.5 137 Factors leading to insulin resistance Insulin resistance may arise from abnormalities in the ... present in the muscle), into sarcoplasmic protein (protein present within the cytosol) and into myosin heavy chain (a key structural and contractile protein) In addition, mitochondria are isolated and...

Ngày tải lên: 09/08/2014, 15:20

... were ineffective In less invasive studies, Borg et al.34 reported an increase in plasma glucose in freely moving rats within 30 minutes of inducing glucopenia in the BRAIN REGIONS INVOLVED IN COUNTER-REGULATION ... ICV injection of insulin reduces food intake and body weight in baboons and rodents171, 172 and administration of anti-insulin antibodies into the rat hypothalamus increases food intake.173 In ... the renin–angiotensin system (RAS), plasminogen activator inhibitor-1 (PAI-1) and more recently omentin and visfatin.79 The role of TNF-α, leptin, Il-6, resistin and adiponectin in linking obesity...

Ngày tải lên: 09/08/2014, 15:20

... correlated to diabetes and insulin resistance in the obese, and administering adiponectin restores insulin sensitivity and assists weight reduction 280 ADIPOKINES AND INSULIN RESISTANCE Treatment ... as inhibiting interactions between other downstream mediators of insulin signalling such as Akt and phosphatidylinositol 3-kinase.111 The ability of IL-6 to induce insulin resistance may be indirect, ... suggests that resistin expression is inhibited in obesity and insulin resistance, and PPARγ agonists (including the TZDs) increase its expression.206 – 209 ADIPOKINES IMPLICATED IN INSULIN RESISTANCE...

Ngày tải lên: 09/08/2014, 15:20

... OGTT–fasting and post-challenge insulin Fasting insulin OGTT–fasting and post-challenge insulin Measure of insulin resistance Table 12.1 (continued ) Age, fasting glucose, BMI, WHR, sum of skin fold, ... Ethnicity: Chinese (Guangdong Province) Participant characteristics Fasting plasma insulin measured on a sub-set of 695 individuals Fasting and h insulin Fasting serum insulin (Fasting insulin resistance ... Ethnicity: Caucasians (New Zealand) h insulin after standard meal (containing 100 g CHO, 30 g fat and 30 g protein) Fasting insulin Stratified by sex Participants taking insulin and hypoglycemic drugs...

Ngày tải lên: 09/08/2014, 15:20

... variation in serum leptin levels and contains several potential candidate genes including the glucokinase regulatory protein and POMC However, it was not significantly linked to hypertension in African-Americans.313 ... Solini, A., Nosadini, R., Goldfine, I D., Vigneri, R and Trischitta, V (1998) Elevated PC-1 content in cultured skin fibroblasts correlates with decreased in vivo and in vitro insulin action in ... also been proposed to link obesity with insulin resistance, with serine phosphorylation of the insulin receptor substrate-1 being a prominent mechanism for TNF-α-induced insulin resistance.228 Physiologically,...

Ngày tải lên: 09/08/2014, 15:20