Using the equals() method with String and Object in Java

equals for Object compares memory references.
That is why it is false since they are different Objects
equals for String is overridden to compare based on characters.
You have 2 empty String objects that is why equals returns true.

Because equals() for String compares the content, not the object itself.

public boolean equals(Object anObject)

Compares this string to the specified object. The result is true if and only if the argument is not null and is a String object that represents the same sequence of characters as this object.

    /* String.equals() */
public boolean equals(Object anObject) {
    if (this == anObject) {
        return true;
    }
    if (anObject instanceof String) {
        String anotherString = (String)anObject;
        int n = count;
        if (n == anotherString.count) {
            char v1[] = value;
            char v2[] = anotherString.value;
            int i = offset;
            int j = anotherString.offset;
            while (n-- != 0) {
                if (v1[i++] != v2[j++])
                    return false;
            }
            return true;
        }
    }
    return false;
}

(Link to the source of String.equals())

Versus the equals for Object:

The equals method for class Object implements the most discriminating possible equivalence relation on objects; that is, for any non-null reference values x and y, this method returns true if and only if x and y refer to the same object (x == y has the value true).

/* Object.equals() */
public boolean equals(Object obj) {
    return (this == obj);
}

(Link to the source of Object.equals())

Also, don't forget the contract of the equals() function:

The equals method implements an equivalence relation on non-null object references:

• It is reflexive: for any non-null reference value x, x.equals(x) should return true.
• It is symmetric: for any non-null reference values x and y, x.equals(y) should return true if and only if y.equals(x) returns true.
• It is transitive: for any non-null reference values x, y, and z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) should return true.
• It is consistent: for any non-null reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals comparisons on the objects is modified.
• For any non-null reference value x, x.equals(null) should return false.

Also recommended reading:

• Object.hashCode()
• Effective Java (Bloch)